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You searched for subject:(Mixing limit). Showing records 1 – 3 of 3 total matches.

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Georgia Tech

1. Diaz-Mercado, Yancy J. Interactions in multi-robot systems.

Degree: PhD, Electrical and Computer Engineering, 2016, Georgia Tech

The objective of this research is to develop a framework for multi-robot coordination and control with emphasis on human-swarm and inter-agent interactions. We focus on two problems: in the first we address how to enable a single human operator to externally influence large teams of robots. By directly imposing density functions on the environment, the user is able to abstract away the size of the swarm and manipulate it as a whole, e.g., to achieve specified geometric configurations, or to maneuver it around. In order to pursue this approach, contributions are made to the problem of coverage of time-varying density functions. In the second problem, we address the characterization of inter-agent interactions and enforcement of desired interaction patterns in a provably safe (i.e., collision free) manner, e.g., for achieving rich motion patterns in a shared space, or for mixing of sensor information. We use elements of the braid group, which allows us to symbolically characterize classes of interaction patterns. We further construct a new specification language that allows us to provide rich, temporally-layered specifications to the multi-robot mixing framework, and present algorithms that significantly reduce the search space of specification-satisfying symbols with exactness guarantees. We also synthesize provably safe controllers that generate and track trajectories to satisfy these symbolic inputs. These controllers allow us to find bounds on the amount of safe interactions that can be achieved in a given bounded domain. Advisors/Committee Members: Egerstedt, Magnus (advisor), Wardi, Yorai (committee member), Yezzi, Anthony (committee member), Ames, Aaron D. (committee member), Zhou, Hao Min (committee member).

Subjects/Keywords: Multi-robot control; Human-swarm interactions; Coverage control; Coverage of time-varying density functions; Braids; Multi-robot mixing; Inter-robot interactions; Mixing limit; Symbolic motion planning

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APA (6th Edition):

Diaz-Mercado, Y. J. (2016). Interactions in multi-robot systems. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/55020

Chicago Manual of Style (16th Edition):

Diaz-Mercado, Yancy J. “Interactions in multi-robot systems.” 2016. Doctoral Dissertation, Georgia Tech. Accessed March 01, 2021. http://hdl.handle.net/1853/55020.

MLA Handbook (7th Edition):

Diaz-Mercado, Yancy J. “Interactions in multi-robot systems.” 2016. Web. 01 Mar 2021.

Vancouver:

Diaz-Mercado YJ. Interactions in multi-robot systems. [Internet] [Doctoral dissertation]. Georgia Tech; 2016. [cited 2021 Mar 01]. Available from: http://hdl.handle.net/1853/55020.

Council of Science Editors:

Diaz-Mercado YJ. Interactions in multi-robot systems. [Doctoral Dissertation]. Georgia Tech; 2016. Available from: http://hdl.handle.net/1853/55020


University of Cincinnati

2. Gonchigdanzan, Khurelbaatar. ALMOST SURE CENTRAL LIMIT THEOREMS.

Degree: PhD, Arts and Sciences : Mathematics, 2001, University of Cincinnati

The almost sure central limit theorem (ASCLT) has been discovered by two works by Brosamler (1988) and Schatte (1988) and extensively studied in the past decade. In the dissertation we investigate ASCLT and its extensions to weakly dependent random variables. Its strong approximation is also considered for both independent and dependent random variables. The goal is to prove ASCLT, 'logarithmic' limit theorems and related invariance principles for weakly dependent random variables. Advisors/Committee Members: Peligrad, Magda (Advisor).

Subjects/Keywords: Mathematics; Statistics; LIMIT THEOREMS; DEPENDEND VARIABLES; ALMOST SURE CENTRAL LIMIT THEOREMS; LOGARITHMIC AVERAGE; G-MIXING, STRONG MIXING, ASSOCIATED VARIABLES

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Gonchigdanzan, K. (2001). ALMOST SURE CENTRAL LIMIT THEOREMS. (Doctoral Dissertation). University of Cincinnati. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=ucin990028192

Chicago Manual of Style (16th Edition):

Gonchigdanzan, Khurelbaatar. “ALMOST SURE CENTRAL LIMIT THEOREMS.” 2001. Doctoral Dissertation, University of Cincinnati. Accessed March 01, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=ucin990028192.

MLA Handbook (7th Edition):

Gonchigdanzan, Khurelbaatar. “ALMOST SURE CENTRAL LIMIT THEOREMS.” 2001. Web. 01 Mar 2021.

Vancouver:

Gonchigdanzan K. ALMOST SURE CENTRAL LIMIT THEOREMS. [Internet] [Doctoral dissertation]. University of Cincinnati; 2001. [cited 2021 Mar 01]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=ucin990028192.

Council of Science Editors:

Gonchigdanzan K. ALMOST SURE CENTRAL LIMIT THEOREMS. [Doctoral Dissertation]. University of Cincinnati; 2001. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=ucin990028192

3. Reding, Lucas. Contributions au théorème central limite et à l'estimation non paramétrique pour les champs de variables aléatoires dépendantes. : Contributions to the central limit theorem and to nonparametric estimation for dependent random fields.

Degree: Docteur es, Mathématiques, 2020, Normandie

La thèse suivante traite du Théorème Central Limite pour des champs de variables aléatoires dépendantes et de son application à l’estimation non-paramétrique. Dans une première partie, nous établissons des théorèmes centraux limite quenched pour des champs satisfaisant une condition projective à la Hannan (1973). Les versions fonctionnelles de ces théorèmes sont également considérées. Dans une seconde partie, nous établissons la normalité asymptotique d’estimateurs à noyau de la densité et de la régression pour des champs fortement mélangeants au sens de Rosenblatt (1956) ou bien des champs faiblement dépendants au sens de Wu (2005). Dans un premier temps, nous établissons les résultats pour l’estimateur à noyau de la régression introduit par Elizbar Nadaraya (1964) et Geoffrey Watson (1964). Puis, dans un second temps, nous étendons ces résultats à une large classe d’estimateurs récursifs introduite par Peter Hall et Prakash Patil (1994).

This thesis deals with the central limit theorem for dependent random fields and its applications to nonparametric statistics. In the first part, we establish some quenched central limit theorems for random fields satisfying a projective condition à la Hannan (1973). Functional versions of these theorems are also considered. In the second part, we prove the asymptotic normality of kernel density and regression estimators for strongly mixing random fields in the sense of Rosenblatt (1956) and for weakly dependent random fields in the sense of Wu (2005). First, we establish the result for the kernel regression estimator introduced by Elizbar Nadaraya (1964) and Geoffrey Watson (1964). Then, we extend these results to a large class of recursive estimators defined by Peter Hall and Prakash Patil (1994).

Advisors/Committee Members: Volny, Dalibor (thesis director), El Machkouri, Mohamed (thesis director).

Subjects/Keywords: Champs de variables aléatoires; Théorème central limite quenched; Théorème central limite fonctionnel quenched; Approximation par ortho-martingale; Condition projective; Estimation non-paramétrique; Estimation de la densité; Estimation de la régression; Estimateur de Nadaraya-Watson; Estimateur récursif; Normalité asymptotique; Données spatiales; Mélange fort; M-dépendance; Mesure de dépendance physique; Dépendance faible; Méthode de Lindeberg; Random fields; Quenched central limit theorem; Quenched functional central limit theorem; Ortho-martingale approximation; Projective condition; Nonparametric estimation; Density estimation; Regression estimation; Nadaraya-Watson estimator; Recursive estimator; Asymptotic normality; Spatial data; Strong mixing; M-dependence; Physical dependence measure; Weak dependence; Linderberg's method; 519.4

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Reding, L. (2020). Contributions au théorème central limite et à l'estimation non paramétrique pour les champs de variables aléatoires dépendantes. : Contributions to the central limit theorem and to nonparametric estimation for dependent random fields. (Doctoral Dissertation). Normandie. Retrieved from http://www.theses.fr/2020NORMR049

Chicago Manual of Style (16th Edition):

Reding, Lucas. “Contributions au théorème central limite et à l'estimation non paramétrique pour les champs de variables aléatoires dépendantes. : Contributions to the central limit theorem and to nonparametric estimation for dependent random fields.” 2020. Doctoral Dissertation, Normandie. Accessed March 01, 2021. http://www.theses.fr/2020NORMR049.

MLA Handbook (7th Edition):

Reding, Lucas. “Contributions au théorème central limite et à l'estimation non paramétrique pour les champs de variables aléatoires dépendantes. : Contributions to the central limit theorem and to nonparametric estimation for dependent random fields.” 2020. Web. 01 Mar 2021.

Vancouver:

Reding L. Contributions au théorème central limite et à l'estimation non paramétrique pour les champs de variables aléatoires dépendantes. : Contributions to the central limit theorem and to nonparametric estimation for dependent random fields. [Internet] [Doctoral dissertation]. Normandie; 2020. [cited 2021 Mar 01]. Available from: http://www.theses.fr/2020NORMR049.

Council of Science Editors:

Reding L. Contributions au théorème central limite et à l'estimation non paramétrique pour les champs de variables aléatoires dépendantes. : Contributions to the central limit theorem and to nonparametric estimation for dependent random fields. [Doctoral Dissertation]. Normandie; 2020. Available from: http://www.theses.fr/2020NORMR049

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